This paper presents several measurements of total production cross sections and total inelastic cross sections for the following reactions:more » $$\pi^{+}$$+C, $$\pi^{+}$$+Al, $$K^{+}$$+C, $$K^{+}$$+Al at 60 GeV/c, $$\pi^{+}$$+C and $$\pi^{+}$$+Al at 31 GeV/c . The measurements were made using the NA61/SHINE spectrometer at the CERN SPS. Comparisons with previous measurements are given and good agreement is seen. Furthermore, these interaction cross sections measurements are a key ingredient for neutrino flux prediction from the reinteractions of secondary hadrons in current and future accelerator-based long-baseline neutrino experiments.« less